Question

If one of the zeroes of the quadratic polunomoals(K-1) x2 +kx+1 is 3 then find the value of k

Answer 1

Given:

• A quadratic polynomial as (k-1)x²+kx+1.
• One of the zeroes is 3.

To Find:

• The value of k.

Concept Used:

• We will put x = 3 in the above equation as 3 is the zero the given quadratic polynomial and ,so we will get value of whole polynomial as 0.

Answer:

Given polynomial to us is , (k-1)x²+kx+1 .

Putting x = 3 ,

$\sf{\implies (k-1)\times(3)^2+3\times k +1=0}$

$\sf{\implies (k-1)\times 9+3k +1=0}$

$\sf{\implies 9k - 9 +3k +1=0}$

$\sf{\implies 12k -8=0}$

$\sf{\implies 12k =8}$

$\sf{\implies k=\cancel{\dfrac{8}{12}}}$

${\underline{\boxed{\red{\sf{\leadsto k=\dfrac{2}{3}}}}}}$

Hence the value of k is ⅔.